The bx36 bus comes every 14 minutes. the bx32 bus comes every 4 minutes. both buses arrive at 4:00pm. what time will it be when both buses arrive at the same time again?

Lets make a time table:

Bx36:4:00, 4:14, 4:28

Bx32:4:00, 4:04, 4:08, 4:12, 4:16, 4:20, 4:24, 4:28

The answer is 4:28pm

The number of times bx36 comes is represented by x

the number of times bx32 comes is represented by y

bx36 times (like 1ocloc, 2 o clock etc) it comes is 14x because if it comes once then 14 mins have passed

likewise with bx32 so 4y

so we want to find when 14x=4y

so we try and solve for when x and y are equal

14x=4y

divide both sides by 2

7x=2y

divide both sides by 2

3.5x=y

subsitute a value for x will yield a whole value

if we multiply. 5 by 2 then it will yield a whole (nondecimal) value

3.5 (2) = 7

the first time is when x=2 and y=7 (followed by (x, y) (2,7) (4,14) (6,21)) so

if x=2 then 14x=14 (2) = 28

4:00+28=4:28

4:28 is the next time